
Concept explainers
Interpretation:
The amount, activity and the probability of
Concept introduction:
The half-life of the reaction is the period of time required for the concentration of a reactant to decrease to one-half of its initial value. It is written as t1/2. Thus, the half-life of a reaction is the time required for the reactant concentration to decrease from [N]0 to [N]0/2.
The amount of a particular radioactive isotope left after time t is given as:
Here,
is the rate constant for the radioactive decay,
Nearly all radioactive decays are of first order and the rate constant is given as:
Here,
is the half -life of the radioactive substance.
The rate of decay for a particular isotope is given by the rate law as:
Here,
is the rate constant for the radioactive decay and

Answer to Problem 88AP
Solution:
Probability is
Explanation of Solution
a) Number of
nuclei left after 30 min.
Half -life of
Initial amount of
nuclei
Time (t)
It is also known that the rate constant for the radioactive decay is given as follows:
Substitute the value of half-life in the above expression, we get rate constant,
Now, the number of Mg present after
is calculated by the expression as follows:
Here,
is the final rate of disintegration or the amount of radioactive substance left after time t.
Substitute the values of
On solving further,
Thus, the number of
is
b) The
At first, convert the rate constant unit into
It is known that one minute is equal to
Thus, the conversion factor is
The above conversion factor of the rate constant can be written as follows:
Now, at
The activity of
Substitute the values of
Now, by the definition of 1 curie,
disintegration occurs per second.
Thus, the conversion factor is
Hence, by using the above conversion factor, the rate can be converted to curie as follows:
Thus, the radioactivity of
at
is
Similarly, at
The activity of
Substitute the values
Now, by the definition of 1 curie,
disintegration occurs per second.
Thus, the conversion factor is
Hence, by using the above conversion factor, the rate can be converted to curie as:
Thus, the radioactivity of
at
is
c) The probability that
From part (b) results, it is known that the rate constant of
is
Thus, it can be said that
are occurring per second.
Hence, the probability of
that decays in
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Chapter 20 Solutions
Chemistry
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